The present article is a continuation of my work [1] demonstrating
natural applications of non-wellfounded sets in logic.

A stream is given as a domain of interpretation for infinitary
propositional logic. This stream is the set of ordered pairs
. 0 is the empty set and
the second component of every pair is taken as its complement in V.

The logical operations are interpreted in V in the manner of post
algebras. Negation is interpreted as complement. `or` is interpreted
as max. and `and` as min. (with special care when one of the terms is
infinite expression i.e., a negation, and for infinitely long
expressions.)

We then show that we get as a special case the generalized post
algebra
Pw described in Urquhart [2] p. 91. This opens the road to
applications of the methods used in Post algebras to streams and
vice-versa.

We then study the extension of these results to predicate logic and
look at its implications on the complexity of the decision problem for
propositional logic by comparing the underlying set theories.

References

1. I. Garro, Resolving paradoxes of self reference using
the
theory of non-wellfounded sets. Submitted to the ASL meeting May
22-25,
Toronto, 1988.